What should we do with 'Important' & 'Optional' updates found in
Windows 8 Update screen after long period of time

We have always had the system download the updates and informed to restart the PC so it can install updates downloaded (and we have had various windows updates recently).

Out of curiosity, we wanted to check if there were any left not installed; we noticed that there is one (1) 'Important' update and seven (7) 'Optional' updates for install.

Since the system always download automatically and we always process the recommended updates, why are these 8 updates not process as the regular periodic updates we get? also, should we proceed to install these 8 updates? (this last question is because in Windows 8 we have had some problem installing updates found in this screen after a period of time).

You should let those install. Use the GPO https://www.vanstechelman.eu/windows-group-policy-encyclopedia/585f0e52252ae3d745dfe29a93143f20/turn-on-recommended-updates-via-automatic-updates to enforce it. Drivers are a bit risky, though, I would only enable this policy if you use WSUS and don't deploy drivers, at least not all drivers.

Forgot to include a pic of the updates found:

Optional updates are not downloaded or installed automatically. How many clients do you have? Is WSUS an option?

You should let those install. Use the GPO https://www.vanstechelman.eu/windows-group-policy-encyclopedia/585f0e52252ae3d745dfe29a93143f20/turn-on-recommended-updates-via-automatic-updates to enforce it. Drivers are a bit risky, though, I would only enable this policy if you use WSUS and don't deploy drivers, at least not all drivers.

What WSUS used for?

i am tempted to say a grinning "you can't be serious" :)Windows Software Update Services is the standard patch management solution for windows.